Modeling familial association of ages at onset of disease in the presence of competing risk

Abstract

In genetic family studies, ages at onset of diseases are routinely collected. Often one is interested in assessing the familial association of ages at the onset of a certain disease type. However, when a competing risk is present and is related to the disease of interest, the usual measure of association by treating the competing event as an independent censoring event is biased. We propose a bivariate model that incorporates two types of association: one is between the first event time of paired members, and the other is between the failure types given the first event time. We consider flexible measures for both types of association, and estimate the corresponding association parameters by adopting the two-stage estimation of Shih and Louis (1995, Biometrics 51, 1384-1399) and Nan et al. (2006, Journal of the American Statistical Association 101, 65-77). The proposed method is illustrated using the kinship data from the Washington Ashkenazi Study.

Figure 1

The non-parametric estimate of the probability of failure type being cancer given the age at onset (solid circle) and a fitted line of a fourth-degree polynomial model to this non-parametric estimate. The fitted model is used in the simulation study to generate the failure type given the age at onset.

Figure 2

Top left: cancer vs. cancer cross-ratio; top right: cancer vs. non-cancer death cross-ratio; bottom left: non-cancer death vs. non-cancer death cross-ratio. The averaged cancer-cancer cross-ratios in the six sub-regions ordered in Table 1 are 1.22, 1.19, 1.29, 1.20, 1.40 and 1.34 with corresponding standard error 0.17, 0.10, 0.11, 0.14, 0.12 and 0.25. The alternative Bandeen-Roche and Ning estimate described in the simulation study in Section 5 equals 2.36, 1.94, 1.80, 1.57, 1.45 and 1.94 with corresponding standard error 0.43, 0.24, 0.28, 0.31, 0.27, and 0.87.

Figure 3

Left panel: marginal and conditional cumulative cancer incidence; right panel: marginal and conditional cumulative non-cancer mortality incidence.

Figure 4

Top: marginal and conditional cumulative cancer incidence given the failure type of the other family member; bottom: marginal and conditional cumulative non-cancer mortality incidence given the failure type of the other family member.

Figure 5

A diagram used to illustrate the order of constructing the bivariate survival function on the boundaries.